Protection of bacteriophage-sensitive Escherichia coli by lysogens

Significance Some viruses that infect bacteria, temperate bacteriophages, can confer immunity to infection by the same virus. Here we report λ-immune bacteria could protect λ-sensitive bacteria from killing by phage λ in mixed culture. The protection depended on the extent to which the immune bacteria were able to adsorb the phage. Reconciling modeling with experiment led to identifying a decline in protection as bacteria stopped growing. Adsorption of λ was compromised by inhibition of bacterial energy metabolism, explaining the loss of protection as bacterial growth ceased.

λcIb221 was a gift from J. Beckwith. It bears the ET22 allele of cI, a C to G transversion at nucleotide 37,810 of the λ + sequence [8] encoding a defective repressor. It is also deleted for the attachment site used by λ to integrate into the bacterial chromosome. We used this version of a λcI phage to reduce the possibility of stable transfer of the cI + allele from the prophage in S3207 to S3137 in the herd immunity experiments.
λh is a host-range mutant described in Materials and Methods. Its complete genotype is λcI b221 J(I1083T) λvir harbors mutant operators preventing λ repressor (CI) from binding to λ DNA. λvir enters lytic development even when infecting a λ lysogen.

Efficiency of transduction by λS3069
λS3069 lysates were titered on S3137. 800 to 3100 PFU/ml were added to a growing 37 • C culture of S3207 at approximately 10 9 CFU/ml in YT broth supplemented with 5 mM MgSO 4 . The mix was incubated at room temperature for 5 minutes then diluted 5 fold with 37 • C YT broth supplemented with 5 mM MgSO 4 . A sample was removed and spread on YT agar supplemented with 50 µg/ml ampicillin. The rest was incubated at 37 • C and samples withdrawn versus time and spread on YT agar supplemented with 50 µg/ml ampicillin. Agar plates were incubated overnight at 37 • C and colonies counted the next day. Results from the first experiment are shown in Figure S2. Here, 40 PFU generated 31 ampicillin-resistant transductants for an efficiency of 78%. In two subsequent experiments we observed 167 ampicillin-resistant transductants from 310 PFU and 157 ampicillin-resistant transductants from 220 PFU for efficiencies of transduction of 54% and 71% respectively. The average efficiency of transduction from the 3 experiments was 68%.
The lag in expression of ampicillin-resistance under these conditions was short relative to the generation time of the bacterium as shown in Figure S2. Time course of R 0 (delayed R 0 ) In our analysis of the initial R 0 (Fig. 3b), we assumed the increase in 37 • C ampicillinresistant CFUs after about 99 minutes was solely due to cell division of transductants formed prior to 98 minutes. A more detailed analysis found new ampicillin-resistant transductants continued to be formed. To observe this, we repeated the temperature-shift experiment with mixed cultures of S3136 and S3207 but at various times diluted the mixed culture into cultures of S3208. Transductants of S3207 and of S3208 were readily distinguished on indicator agar by the color of the colonies (Fig. S1).
We first repeated the assay we used to determine an initial R 0 replacing the rich agar with selective indicator agar which was indicator agar supplemented with 100 µg/ml each, ampicillin and streptomycin. S3136 was streptomycin-sensitive and S3207 was streptomycinresistant. Here we found an initial R 0 of between 7.8 and 11.5. This value was consistent with our determination of 9.0 -10.7 on rich agar and indicated we could perform the time course on selective indicator agar.
We next repeated the R 0 measurements but in addition to diluting and spreading the mixed 37 • C cultures of S3136 and S3207 on selective indicator agar, we diluted the mixed cultures into a growing culture of S3208. After 10 minutes further incubation with S3208, we spread samples onto selective indicator agar. Throughout the latter period we detected newly formed transductants of S3208 as blue colonies on selective indicator agar at 37 • C. We quantified the rate of continued transduction of S3207 by comparing the rate of formation of ampicillin-resistant colonies with the growth rate of the mixed, predominantly S3207, culture as monitored by turbidity. To determine the ratio of S3207 and S3208, samples were withdrawn at time of mixing and optical density at 600nm determined. Unlike in our initial measurements of R 0 , the selective indicator agar plates were incubated 2 days at 37 • C and transductants of S3207 and S3208 were counted as white and blue colonies, respectively.
The results from one time course experiment are shown in Fig. S3 panels A and B. The mixed culture, predominantly S3207, grew with a doubling time of 29 minutes as determined by increase in absorbance at 600nm. The transductants selected on the agar used in these experiments appeared with an apparent doubling time of 18 minutes from 80 to 120 minutes after temperature shift. The additional growth was probably due to continued transduction as diluting the mixed culture 10 fold into a culture of S3208 generated blue, ampicillin-and streptomycin-resistant transductants over this same period. We are unable to explain the great fluctuations in the appearance of blue transductants and only interpret their appearance to indicate continued active transduction. Also, their continued appearance after the rapid rise of transductants ceased indicates our determination of additional R 0 below may represent a minimum value.
To determine the additional R 0 , we assumed transductants appearing by 80 minutes grew with a doubling time of 29 minutes. Thus, excess transductants appearing up to 120 minutes were assumed to be due to new transductions. The 29 minute doubling time predicted 14,300 transductants per ml at 120 minutes but we observed 25,500 transductants per ml for an excess of 11,200 transductants per ml. If each transductant grew with a doubling time of 29 minutes over the 40 minute period and since the sum of n = 1 to n = 40 of 2 (n/29) is 68, we expected 11,200/68 or 165 transductants per ml per minute from the 947 "primary case" S3136 CFU/ml. This resulted in a delayed R 0 of 0.174 transductants per ml per min  (Fig. S4). The additional infections over the period from the second to the third cell generation would be approximately the average of the two above infections per minute times 24 minutes, generating an additional R 0 of approximately 3.6 for transduction of ampicillin-resistance by λS3069.

Burst size corrections
The killing we observed in Figure 2 predicts a much larger value for R 0 than 10.7. To test if this value for R 0 was artificially low due to a difference between the prophage in S3136 and λcIb221 we compared three properties of the two systems, burst size, efficiency of transduction of ampicillin-resistance and phenotypic lag of ampicillin-resistance.
To compare burst size we compared S3136 with that of our sensitive host harboring a more wild-type prophage, S3224. S3224 harbors λcI857 (see strain descriptions above). YT broth cultures of S3136 or S3224 were established at 30 • C from independent colonies. After overnight growth they were diluted 40 fold into YT broth supplemented with 5 mM MgSO 4 and grown 1 hour at 30 • C. A sample was withdrawn and diluted 100 fold into 4 • C M63 salts and the rest temperature-shifted as for the R 0 measurements. When the cultures cleared lysis was completed with a drop of CHCl 3 and passed through 0.45 µm sterile filters. Diluted samples of the 30 • C cultures were diluted further in M63 salts and spread on YT agar to determine the CFU/ml. The filtrates were diluted with TMG [9] and titered on S3137 to determine PFU/ml. Burst size was determined as PFU/30 • C CFU.
In two experiments, the first with 3 independent cultures of each and the second with 2 independent cultures of each, we found λcI857 generated burst sizes 2.7 times and 2.9 times the burst size of λS3069, the resident prophage in S3136. The efficiency of packaging of λ phage DNA declines with genome length for phages having larger genomes than wild-type [10]. The DNA of λS3069 is 51,446 base pairs [2] which is 6% longer than wild-type λ DNA and therefore expected to have a smaller burst size.
We measured the efficiency of transduction of ampicillin-resistance of λS3069 phages. In lysates of λS3069 we found the number of transducing units per ml to be approximately 68% the number of PFU per ml. The phenotypic lag for resistance to 50 µg/ml of ampicillin on YT agar represented only a few percent of a generation time (Fig. S2) and was not considered further. Combining corrections for burst size and efficiency of transduction increases the measured initial R 0 of 9.0 -10.7 for λS3069 by 4.1 fold (2.8/0.68) to 37 -44 for λcIb221. Applying the same correction factors for the delayed R 0 raised the R 0 for λcIb221 by approximately 15 over the next bacterial generation. That is, while 15 secondary infections were generated, the host population doubled.

Departure from exponential growth
This experiment focused on the departure from exponential growth of a mixed culture containing the λ-sensitive strain, S3137, and the λ-immune strain, S3207. The experiment was performed as in the herd immunity experiments except only the uninfected mixed culture was examined. The mixed culture was initiated with 7% S3137 and sampling focused on the period the mixed culture departed exponential growth. S3137 growth as blue CFU/ml is shown as squares and S3207 growth as white CFU/ml is shown as circles. In Fig. S4(a), the lines represent a least squares fit to the data from 0 to 200 minutes. The lower line represents a doubling time of 23.1 minutes and the upper line a doubling time of 28.1 minutes. That is, the doubling time of S3207 was approximately 1.2 fold longer than that of S3137 during the majority of exponential growth. In Fig. S4(b), only the period as growth slowed is illustrated. Here it appears growth of S3207 slowed more rapidly than that of S3137. The lower line represents a doubling time of 31.8 minutes and the upper line a doubling time of 32.2 minutes.

Infection rate
We measured how the infection rate varied with cell concentration. We measured transduction of ampicillin-resistance into the immune strain, S3207, by λS3069. Overnight cultures of S3207 grown in YT broth 30 • C were diluted into YT broth supplemented with 5 mM MgSO 4 and incubated at 37 • C as in the infection of mixed populations and R 0 experiments. Various dilutions of the culture in YT broth supplemented with 5 mM MgSO 4 were mixed with either λS3069 diluted in YT broth supplemented with 5 mM MgSO 4 or with YT broth supplemented with 5 mM MgSO 4 alone. After 5 and 20 minutes of incubation at 37 • C with shaking, samples were withdrawn and diluted 10 fold into 1xM63 salts at 4 • C. Samples were spread on YT agar supplemented with 50 µg/ml ampicillin or diluted further in 1xM63 salts and spread on YT agar. Plates were incubated overnight at 37 • C and colonies were counted. Phage samples were diluted in TMG and titered on S3137.

Relative infectability
We compared the infectability of a derivative of the sensitive strain, S3137, with the immune strain, S3207. S3223 is S3137(λ + ). Since the competitor strain, S3207, is λ-immune, the results would not be confused by λ + released from S3223 conferring immunity on S3207. We performed an initial measurement infecting a mixed culture of S3207 and S3223 with the ampicillin-resistance transducing phage, λS3069, to optimize experimental parameters. The preliminary experiment found S3223 acquired ampicillin-resistance approximately 1.8 times as frequently as S3207. We then performed the more careful measurement below using both independent bacterial cultures and independent lysates of λS3069.
Exponential phase cultures in YT broth supplemented with 5 mM MgSO 4 were established at 37 • C for each strain. They were mixed and diluted into the same medium and grown together for an hour at 37 • C. Samples of the mixed cultures were then mixed with either YT broth supplemented with 5 mM MgSO 4 or λS3069 diluted into the same. The initial bacterial concentrations were approximately 10 8 CFU/ml. Samples were immediately withdrawn to determine the MOI based on viable cell counts. The samples were then incubated with shaking at 37 • C.
After 15 minutes samples were removed and diluted 10 fold into M63 salts at 4 • C. Samples were diluted further and spread on indicator agar to determine the ratio of S3137(λ + ) (blue colonies) to S3207 (white colonies). Samples were also spread on indicator agar supplemented with 50 µg/mL ampicillin and incubated at 37 • C to examine transductants. The results of the second experiment are shown below. Samples of the mixed bacterial mixed cultures mixed with broth instead of phage or the phage lysates mixed with broth instead of bacteria generated no ampicillin-resistant colonies. Uninfected culture A had a blue/white ratio of 0.586 at 15 minutes. Uninfected culture B had a blue/white ratio of 0.617 at 15 minutes. The average blue/white ratio among ampicillin-resistant transductants was 1.7 times the blue/white ratio in the absence of added phages and ampicillin. That is, S3223 was infected 1.7 times as often as S3207.

Energy-dependence of adsorption
Herd immunity provided by the λ-immune bacteria declined on departure from exponential growth. To test if adsorption of the phage to the bacteria could cause this departure, we measured adsorption [11] of λ in an energy producing state, in the presence of glucose, and in an energy depleted state, in the absence of glucose but in the presence of potassium arsenate and sodium azide. We performed the experiment 3 times, each bacterial culture was initiated from an independent single colony and each phage lysate was initiated from an independent plaque. Exponentially growing cultures in YT broth were centrifuged (1700 x g, 5 minutes, room temperature) washed with 1/2 volume TMG7.6 (20 mM Tris-HCl pH 7.6, 5 mM MgCl 2 , 0.1 mg/ml gelatin) and resuspended with 1/4 volume same. 400 µl of resuspended bacteria or TMG7.6 without bacteria were distributed to 2 ml Eppendorf centrifuge tubes. Either 50 µl of TMG7.6 made 2% w/v glucose and 10 mM potassium phosphate pH 7.4 or 50 µl of TMG7.6 made 10 mM in KH 2 AsO 4 and 0.2 M NaN 3 were added and the mixtures incubated 10 minutes at 37°C with shaking at 300 RPM. Phage diluted in TMG were added to the indicated MOI. The final concentration of bacteria as determined by counting in a Petroff-Hausser chamber was approximately 3 x 10 9 /ml. Incubation with phage was continued for 10 minutes at 37°C with shaking and the bacteria removed by centrifugation at 3,400 x g for 5 minutes at room temperature. 100 µl of the supernatant was aspirated and diluted into 900 µl TMG supplemented with 1 mM potassium phosphate pH 7.4. Further dilutions were prepared in TMG and the phage concentrations determined by spotting 10 µl samples on lawns of S2153. The fraction of phage unbound was the supernatant concentration as PFU/ml in the bacteria-containing mixes divided by the concentration as PFU/ml in the bacteria-free mixes. The results find adsorption by λcIb221 is much more sensitive to arsenate and azide than λh and the adsorption requires LamB.

Pilot studies
In our initial efforts to develop the herd immunity assay, we conducted the experiment as shown in Fig. 2 but varied not only the initial fraction sensitive bacteria but also MOI and burst size. To obtain the most accurate survival data in mixed cultures we wanted to be able to quantify both the sensitive and immune strains in the same sample. That is, we wanted to be able to count colonies generated from both on the same plates spread with dilutions of the mixed culture. As described in Fig S1, we did this by using indicator agar where the Lac + strain formed blue colonies and the Lacstrain formed white colonies. As we expected the majority of both the initial and surviving populations to be the immune strain, we used a Lac + (blue) sensitive strain and a Lac -(white) immune strain. Experiment 1 used λcIb221 but a different λ-sensitive strain, S3181, than used for Fig. 2. In experiment 2 we reduced the burst size by replacing λcIb221 with λcI A(am)11 nin5. The nonsense allele of A is well suppressed by the tyrosine-inserting suppressor tRNA encoded by supF but poorly suppressed by the glutamine-inserting suppressor tRNA encoded by supE. Lysates of λcI A(am)11 nin5 prepared on the supF strain S2152 form the same number of plaques on S2152 as on S3137 but the plaques are much smaller on S3137 suggesting a smaller burst size on S3137.

Theoretical analysis
Continuous time modeling using ordinary differential equations Virus and host growth are not completely synchronous and the latency time between infection and virus production is distributed. To take into account such a continuous nature of the process, we considered a set of ordinary differential equations which have been used to analyze the well-mixed phage-bacteria system in a broth culture. The main variables include the concentrations of the sensitive hosts, S, the immune hosts, L (lysogens), and the virus, V . Focusing on the exponential phase of growth, we assumed the growth rates of the sensitive hosts, g S , and and the immune hosts, g L , are constant. We also assumed that when a sensitive host is infected, it passes through M sequential steps of an infected state before bursting to produce progeny viruses. The number of the steps M were used to adjust the spread of the latency time. The set of equations we used: Here, the average latency time between the infection and the virus production is parameterized by τ l , and the multiple steps of the infected state control the latency time distribution [12]. The parameters η S and η L characterize the virus infection rate to the sensitive hosts and the immune hosts, respectively.
Fitting the latency time distribution using the growth curve of infected S3137 We determined the latency time distribution by monitoring the change in turbidity of a bacterial culture with and without added phages. A culture of S3137 growing at 37 • C in YT broth supplemented with 5 mM MgSO 4 was diluted into same with or without λcIb221 to attain concentrations of 6 x 10 7 bacteria per ml and 6 x 10 8 PFU/ml. The mixes were incubated 5 minutes at room temperature at which λ adsorbs to the bacteria but remains in a lag period before injection of the phage DNA [13]. The mixes were shifted to 37 • C to initiate injection and incubated with aeration at 37 • C. Versus time, samples were removed and mixed with an equal volume of 1xM63 salts made 300 µg/ml in chloramphenicol and maintained at 2 • C. A600 was measured versus YT 5 mM MgSO 4 mixed with an equal volume of 1xM63 salts made 300 µg/ml in chloramphenicol. The data is shown in Fig. S5, where time is measured in minutes after shift to 37 • C.
The case without phage was fitted by an exponential curve. The data points up to 80 minutes followed a single exponential curve. It was used for the fitting by the least-squares The last data point that shows A600 below 0.01 is also not fitted, perhaps because such a low adsorption can be due to cell debris. Hence, the fitting was done for the 3 data points between 40 min and 80 min.
Marquardt-Levenberg algorithm provided in gnuplot [14]. This analysis gave the growth rate g S = log(2)/23.5(/min) (i.e., the doubling time τ s = 23.5 min), which is shown as a solid straight line. The case with phage was fitted by the original model (1)-(5) with an initial condition where there are only just infected cells (S(0) = 0, L(0) = 0, I 1 (0) = 1, I j (0) = 0 for later latency stages j = 2, · · · , M , P (0) = 0). Because the model considers phage production per infected bacterium and does not consider bacterial growth and division early after infection, the initial part of the absorbance simulation of infected bacteria was not fitted.
The last data point that shows A600 below 0.01 is also not fitted, perhaps because such a low adsorbance could have been due to cell debris. Hence, the fitting was done for the 3 data points between 40 and 80 minutes. The fitting parameters were the average latency time τ l , the number of infection step M , and the constant factor C to scale cell density and A 600 . For a given parameter set, the total cell density at time t, T (t) = M j=1 I j (t), was computed, and the distance from the log scale for the each measurement time point t k (k = 1, 2, 3 represents the 3 data points) was calculated as δ = 3 k=1 (log(C × T (t)) − log(A 600 (t k )) 2 . We next searched for the parameter set that gave a minimum δ. We found M = 8 and M = 9 gave a similarly good fit with τ l = 2.1 × 23.5 (min) and τ l = 2.2 × 23.5(min), respectively. The shown fit in Fig. S5 is M = 8 case. In the following, we used the M = 8 fit.

Fitting to the infection rate measurement
Next we used a modified model to analyze the infection rate measurement experiment in Table S3. In this experiment, the recipient strain, the strain that was that infected by the phages, was immune. That is, the phages can only infect the initial cells and not propagate. The criterion for survival upon exposure to antibiotics is to have been infected the virus. At time zero, phages are mixed with the recipient strain cells, and the free phage concentration decays as they infect the cells. We used the following set of equations to describe this situation: Here, L is the original recipient that has not been infected, while R is the infected recipient. At time zero, the infected recipient R(0) = 0. This model is analytically solvable, for the initial concentration of the recipient L(0) = L 0 (CFU/ml) and the phage V (0) = V 0 (PFU/ml), the solution is given by where t dt is the exponential integral. We fitted the solution R(t) to the data in Table S3 to find the best values for the growth rate g 0 and the infection rate η L . The goodness of the fit was evaluated by minimizing the distance between the measured ampicillin registrant cells per ml at time t k , ampR(t k ), and the theoretical prediction R(t k ) as δ = [log(0.68R(t k )) − log(ampR(t k ))] 2 . Here, the factor 0.68 is the efficiency of plating for ampicillin-resistance (see main text). The sum was taken for all initial concentrations, the measurement time points t k (5 min and 20 min), and the two experimental data sets. Because the CFU/ml at time t 0 in the table was measured for the sample at 5min, the initial condition L 0 was evaluated as that CFU value multiplied by e −g 0 ×5(min) . We have obtained η L = 6.5 × 10 −10 ml/min and g 0 = log(2)/25(/min) as the best fit. The comparison between the fitted curve and the experimental data points are showin in Fig. S6. In the following, we set η L = 6.5 × 10 −10 ml/min as the infection rate for the immune strain.
Fitting to the R 0 measurement Next we used the slightly modified full model to simulate the R 0 measurement experiment. Instead of the sensitive strain, we have a donor strain that at time zero is set to the "infected" state 1. The recipient will be infected by the phage but they are immune. The criterion for survival upon exposure to antibiotics is to have been infected the virus, as in the infection rate measurement. The donor did not absorb the phages. Therefore, we use the following  Table S3) and the fitted curve (lines). The color indicates the correspondence between the data and the fit. The initial bacteria density was 1.1 × 10 7 CFU/ml, 3.4 × 10 7 CFU/ml, 9.0 × 10 7 CFU/ml and 22 × 10 7 from bottom to top respectively into S3137. Infecting phage density was always 1.0 × 10 5 PFU/ml. model to simulate the R 0 measurement: Here, L represents the original recipient that has not been infected, and R the infected recipient. We have two independent experimental data sets, and fitting was done for each data set separately. First, the growth rate g 0 was estimated by fitting to the exponential function to the OD curve by the least-squares Marquardt-Levenberg algorithm provided by gnuplot. We have obtained g 0 = log(2)/31 (1/min) and g 0 = log(2)/24 (1/min) for experiment 1 and 2, respectively (Fig. S7). We then use M = 8 and τ l = 2.1×log(2)/g 0 , as obtained by the fitting to the latency time distribution of infected S3137. Because the R 0 measurement was done by prophage induction and induction requires additional time for the prophage to be ready to reproduce, we added this additional time t w as a fitting parameter. In the model, t w is the time between the temperature shift and the start of the lysis process. The distributed production of infected cells R comes from this delay time plus the latency time distribution.
The initial conditions used for measuring the delayed R 0 (Fig. S3) were used to simulate the observed results. That is, the initial conditions for experiment 1 used L(0) = 1.0 × 10 7 (/ml), I 1 (0) = 947 (/ml) and for experiment 2 used L(0) = 3.8 × 10 6 (/ml) and I 1 (0) = 793 (/ml). The infection rate determined in the previous section, η L = Amp i (t k ) is the ampicillin resistant CFU/ml for experiment i at time point t k , and N i k is CFU counted on the plate to take into account the error due to limited sampling. The factor 0.68 is the efficiency of plating for ampicillin-resistance (see main text). As the best fit, we have obtained the delay time t w = 17 min and the bust size per donor β = 21. The comparison between the experimental data and the fit is shown in Fig. S7.
Using the fitted parameters, we have simulated how the "R 0 " defined as the number of newly infected recipient cells per donor cell changes over time. We set the burst size to be β = 21 × 2.8 = 58.8, where the factor 2.8 is from the burst size correction between the donor strain in the R 0 measurement and the sensitive strain used in this experiment (see main text). The result is shown in Fig. S8 left. Here, we have used the growth rate to be g 0 = log(2)/30min, and We set t w = 0, i.e., donors are assumed to be just infected at time zero and immediately move to the phage production process. We set the initial amount of the donor cells to be I 1 (0) = 10 4 /ml. We see the low recipient density gives a significant delay in the rise of "R 0 ", while for high initial density "R 0 " quickly saturates to the burst size β ≈ 59. To visualize this initial density dependence clearer, we also show "R 0 " at the time point 2τ l , the time scale at which the next round of burst would start if the newly infected cells were sensitive, as a function of initial recipient density (Fig. S8 right).